arXiv:1712.01168v2 [gr-qc] 2 May 2018
Dated: May 3, 2018
Constraints on cosmic strings using data from the first Advan
ced LIGO observing run.
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
F. Acernese,
3
,
4
K. Ackley,
5
C. Adams,
6
T. Adams,
7
P. Addesso,
8
R. X. Adhikari,
1
V. B. Adya,
9
C. Affeldt,
9
M. Afrough,
10
B. Agarwal,
11
M. Agathos,
12
K. Agatsuma,
13
N. Aggarwal,
14
O. D. Aguiar,
15
L. Aiello,
16
,
17
A. Ain,
18
P. Ajith,
19
B. Allen,
9
,
20
,
21
G. Allen,
11
A. Allocca,
22
,
23
P. A. Altin,
24
A. Amato,
25
A. Ananyeva,
1
S. B. Anderson,
1
W. G. Anderson,
20
S. Antier,
26
S. Appert,
1
K. Arai,
1
M. C. Araya,
1
J. S. Areeda,
27
N. Arnaud,
26
,
28
K. G. Arun,
29
S. Ascenzi,
30
,
17
G. Ashton,
9
M. Ast,
31
S. M. Aston,
6
P. Astone,
32
P. Aufmuth,
21
C. Aulbert,
9
K. AultONeal,
33
A. Avila-Alvarez,
27
S. Babak,
34
P. Bacon,
35
M. K. M. Bader,
13
S. Bae,
36
P. T. Baker,
37
,
38
F. Baldaccini,
39
,
40
G. Ballardin,
28
S. W. Ballmer,
41
S. Banagiri,
42
J. C. Barayoga,
1
S. E. Barclay,
43
B. C. Barish,
1
D. Barker,
44
F. Barone,
3
,
4
B. Barr,
43
L. Barsotti,
14
M. Barsuglia,
35
D. Barta,
45
J. Bartlett,
44
I. Bartos,
46
R. Bassiri,
47
A. Basti,
22
,
23
J. C. Batch,
44
C. Baune,
9
M. Bawaj,
48
,
40
M. Bazzan,
49
,
50
B. B ́ecsy,
51
C. Beer,
9
M. Bejger,
52
I. Belahcene,
26
A. S. Bell,
43
B. K. Berger,
1
G. Bergmann,
9
C. P. L. Berry,
53
D. Bersanetti,
54
,
55
A. Bertolini,
13
J. Betzwieser,
6
S. Bhagwat,
41
R. Bhandare,
56
I. A. Bilenko,
57
G. Billingsley,
1
C. R. Billman,
5
J. Birch,
6
R. Birney,
58
O. Birnholtz,
9
S. Biscans,
14
A. Bisht,
21
M. Bitossi,
28
,
23
C. Biwer,
41
M. A. Bizouard,
26
J. K. Blackburn,
1
J. Blackman,
59
C. D. Blair,
60
D. G. Blair,
60
R. M. Blair,
44
S. Bloemen,
61
O. Bock,
9
N. Bode,
9
M. Boer,
62
G. Bogaert,
62
A. Bohe,
34
F. Bondu,
63
R. Bonnand,
7
B. A. Boom,
13
R. Bork,
1
V. Boschi,
22
,
23
S. Bose,
64
,
18
Y. Bouffanais,
35
A. Bozzi,
28
C. Bradaschia,
23
P. R. Brady,
20
V. B. Braginsky
∗
,
57
M. Branchesi,
65
,
66
J. E. Brau,
67
T. Briant,
68
A. Brillet,
62
M. Brinkmann,
9
V. Brisson,
26
P. Brockill,
20
J. E. Broida,
69
A. F. Brooks,
1
D. A. Brown,
41
D. D. Brown,
53
N. M. Brown,
14
S. Brunett,
1
C. C. Buchanan,
2
A. Buikema,
14
T. Bulik,
70
H. J. Bulten,
71
,
13
A. Buonanno,
34
,
72
D. Buskulic,
7
C. Buy,
35
R. L. Byer,
47
M. Cabero,
9
L. Cadonati,
73
G. Cagnoli,
25
,
74
C. Cahillane,
1
J. Calder ́on Bustillo,
73
T. A. Callister,
1
E. Calloni,
75
,
4
J. B. Camp,
76
M. Canepa,
54
,
55
P. Canizares,
61
K. C. Cannon,
77
H. Cao,
78
J. Cao,
79
C. D. Capano,
9
E. Capocasa,
35
F. Carbognani,
28
S. Caride,
80
M. F. Carney,
81
J. Casanueva Diaz,
26
C. Casentini,
30
,
17
S. Caudill,
20
M. Cavagli`a,
10
F. Cavalier,
26
R. Cavalieri,
28
G. Cella,
23
C. B. Cepeda,
1
L. Cerboni Baiardi,
65
,
66
G. Cerretani,
22
,
23
E. Cesarini,
30
,
17
S. J. Chamberlin,
82
M. Chan,
43
S. Chao,
83
P. Charlton,
84
E. Chassande-Mottin,
35
D. Chatterjee,
20
B. D. Cheeseboro,
37
,
38
H. Y. Chen,
85
Y. Chen,
59
H.-P. Cheng,
5
A. Chincarini,
55
A. Chiummo,
28
T. Chmiel,
81
H. S. Cho,
86
M. Cho,
72
J. H. Chow,
24
N. Christensen,
69
,
62
Q. Chu,
60
A. J. K. Chua,
12
S. Chua,
68
A. K. W. Chung,
87
S. Chung,
60
G. Ciani,
5
R. Ciolfi,
88
,
89
C. E. Cirelli,
47
A. Cirone,
54
,
55
F. Clara,
44
J. A. Clark,
73
F. Cleva,
62
C. Cocchieri,
10
E. Coccia,
16
,
17
P.-F. Cohadon,
68
A. Colla,
90
,
32
C. G. Collette,
91
L. R. Cominsky,
92
M. Constancio Jr.,
15
L. Conti,
50
S. J. Cooper,
53
P. Corban,
6
T. R. Corbitt,
2
K. R. Corley,
46
N. Cornish,
93
A. Corsi,
80
S. Cortese,
28
C. A. Costa,
15
M. W. Coughlin,
69
S. B. Coughlin,
94
,
95
J.-P. Coulon,
62
S. T. Countryman,
46
P. Couvares,
1
P. B. Covas,
96
E. E. Cowan,
73
D. M. Coward,
60
M. J. Cowart,
6
D. C. Coyne,
1
R. Coyne,
80
J. D. E. Creighton,
20
T. D. Creighton,
97
J. Cripe,
2
S. G. Crowder,
98
T. J. Cullen,
27
A. Cumming,
43
L. Cunningham,
43
E. Cuoco,
28
T. Dal Canton,
76
S. L. Danilishin,
21
,
9
S. D’Antonio,
17
K. Danzmann,
21
,
9
A. Dasgupta,
99
C. F. Da Silva Costa,
5
V. Dattilo,
28
I. Dave,
56
M. Davier,
26
D. Davis,
41
E. J. Daw,
100
B. Day,
73
S. De,
41
D. DeBra,
47
J. Degallaix,
25
M. De Laurentis,
75
,
4
S. Del ́eglise,
68
W. Del Pozzo,
53
,
22
,
23
T. Denker,
9
T. Dent,
9
V. Dergachev,
34
R. De Rosa,
75
,
4
R. T. DeRosa,
6
R. DeSalvo,
101
J. Devenson,
58
R. C. Devine,
37
,
38
S. Dhurandhar,
18
M. C. D ́ıaz,
97
L. Di Fiore,
4
M. Di Giovanni,
102
,
89
T. Di Girolamo,
75
,
4
,
46
A. Di Lieto,
22
,
23
S. Di Pace,
90
,
32
I. Di Palma,
90
,
32
F. Di Renzo,
22
,
23
Z. Doctor,
85
V. Dolique,
25
F. Donovan,
14
K. L. Dooley,
10
S. Doravari,
9
I. Dorrington,
95
R. Douglas,
43
M. Dovale
́
Alvarez,
53
T. P. Downes,
20
M. Drago,
9
R. W. P. Drever
♯
,
1
J. C. Driggers,
44
Z. Du,
79
M. Ducrot,
7
J. Duncan,
94
S. E. Dwyer,
44
T. B. Edo,
100
M. C. Edwards,
69
A. Effler,
6
H.-B. Eggenstein,
9
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
5
R. A. Eisenstein,
14
R. C. Essick,
14
Z. B. Etienne,
37
,
38
T. Etzel,
1
M. Evans,
14
T. M. Evans,
6
M. Factourovich,
46
V. Fafone,
30
,
17
,
16
H. Fair,
41
S. Fairhurst,
95
X. Fan,
79
S. Farinon,
55
B. Farr,
85
W. M. Farr,
53
E. J. Fauchon-Jones,
95
M. Favata,
103
M. Fays,
95
H. Fehrmann,
9
J. Feicht,
1
M. M. Fejer,
47
A. Fernandez-Galiana,
14
I. Ferrante,
22
,
23
E. C. Ferreira,
15
F. Ferrini,
28
F. Fidecaro,
22
,
23
I. Fiori,
28
D. Fiorucci,
35
R. P. Fisher,
41
M. Fitz-Axen,
42
R. Flaminio,
25
,
104
M. Fletcher,
43
H. Fong,
105
P. W. F. Forsyth,
24
S. S. Forsyth,
73
J.-D. Fournier,
62
S. Frasca,
90
,
32
F. Frasconi,
23
Z. Frei,
51
A. Freise,
53
R. Frey,
67
V. Frey,
26
E. M. Fries,
1
P. Fritschel,
14
V. V. Frolov,
6
P. Fulda,
5
,
76
M. Fyffe,
6
H. Gabbard,
9
M. Gabel,
106
B. U. Gadre,
18
S. M. Gaebel,
53
J. R. Gair,
107
L. Gammaitoni,
39
M. R. Ganija,
78
S. G. Gaonkar,
18
F. Garufi,
75
,
4
S. Gaudio,
33
G. Gaur,
108
V. Gayathri,
109
N. Gehrels
†
,
76
G. Gemme,
55
E. Genin,
28
A. Gennai,
23
D. George,
11
J. George,
56
L. Gergely,
110
V. Germain,
7
S. Ghonge,
73
Abhirup Ghosh,
19
Archisman Ghosh,
19
,
13
S. Ghosh,
61
,
13
J. A. Giaime,
2
,
6
K. D. Giardina,
6
A. Giazotto
§
,
23
K. Gill,
33
L. Glover,
101
E. Goetz,
9
R. Goetz,
5
S. Gomes,
95
G. Gonz ́alez,
2
2
J. M. Gonzalez Castro,
22
,
23
A. Gopakumar,
111
M. L. Gorodetsky,
57
S. E. Gossan,
1
M. Gosselin,
28
R. Gouaty,
7
A. Grado,
112
,
4
C. Graef,
43
M. Granata,
25
A. Grant,
43
S. Gras,
14
C. Gray,
44
G. Greco,
65
,
66
A. C. Green,
53
P. Groot,
61
H. Grote,
9
S. Grunewald,
34
P. Gruning,
26
G. M. Guidi,
65
,
66
X. Guo,
79
A. Gupta,
82
M. K. Gupta,
99
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
113
B. R. Hall,
64
E. D. Hall,
1
G. Hammond,
43
M. Haney,
111
M. M. Hanke,
9
J. Hanks,
44
C. Hanna,
82
M. D. Hannam,
95
O. A. Hannuksela,
87
J. Hanson,
6
T. Hardwick,
2
J. Harms,
65
,
66
G. M. Harry,
114
I. W. Harry,
34
M. J. Hart,
43
C.-J. Haster,
105
K. Haughian,
43
J. Healy,
115
A. Heidmann,
68
M. C. Heintze,
6
H. Heitmann,
62
P. Hello,
26
G. Hemming,
28
M. Hendry,
43
I. S. Heng,
43
J. Hennig,
43
J. Henry,
115
A. W. Heptonstall,
1
M. Heurs,
9
,
21
S. Hild,
43
D. Hoak,
28
D. Hofman,
25
K. Holt,
6
D. E. Holz,
85
P. Hopkins,
95
C. Horst,
20
J. Hough,
43
E. A. Houston,
43
E. J. Howell,
60
Y. M. Hu,
9
E. A. Huerta,
11
D. Huet,
26
B. Hughey,
33
S. Husa,
96
S. H. Huttner,
43
T. Huynh-Dinh,
6
N. Indik,
9
D. R. Ingram,
44
R. Inta,
80
G. Intini,
90
,
32
H. N. Isa,
43
J.-M. Isac,
68
M. Isi,
1
B. R. Iyer,
19
K. Izumi,
44
T. Jacqmin,
68
K. Jani,
73
P. Jaranowski,
116
S. Jawahar,
117
F. Jim ́enez-Forteza,
96
W. W. Johnson,
2
D. I. Jones,
118
R. Jones,
43
R. J. G. Jonker,
13
L. Ju,
60
J. Junker,
9
C. V. Kalaghatgi,
95
V. Kalogera,
94
S. Kandhasamy,
6
G. Kang,
36
J. B. Kanner,
1
S. Karki,
67
K. S. Karvinen,
9
M. Kasprzack,
2
M. Katolik,
11
E. Katsavounidis,
14
W. Katzman,
6
S. Kaufer,
21
K. Kawabe,
44
F. K ́ef ́elian,
62
D. Keitel,
43
A. J. Kemball,
11
R. Kennedy,
100
C. Kent,
95
J. S. Key,
119
F. Y. Khalili,
57
I. Khan,
16
,
17
S. Khan,
9
Z. Khan,
99
E. A. Khazanov,
120
N. Kijbunchoo,
44
Chunglee Kim,
121
J. C. Kim,
122
W. Kim,
78
W. S. Kim,
123
Y.-M. Kim,
86
,
121
S. J. Kimbrell,
73
E. J. King,
78
P. J. King,
44
R. Kirchhoff,
9
J. S. Kissel,
44
L. Kleybolte,
31
S. Klimenko,
5
P. Koch,
9
S. M. Koehlenbeck,
9
S. Koley,
13
V. Kondrashov,
1
A. Kontos,
14
M. Korobko,
31
W. Z. Korth,
1
I. Kowalska,
70
D. B. Kozak,
1
C. Kr ̈amer,
9
V. Kringel,
9
B. Krishnan,
9
A. Kr ́olak,
124
,
125
G. Kuehn,
9
P. Kumar,
105
R. Kumar,
99
S. Kumar,
19
L. Kuo,
83
A. Kutynia,
124
S. Kwang,
20
B. D. Lackey,
34
K. H. Lai,
87
M. Landry,
44
R. N. Lang,
20
J. Lange,
115
B. Lantz,
47
R. K. Lanza,
14
A. Lartaux-Vollard,
26
P. D. Lasky,
126
M. Laxen,
6
A. Lazzarini,
1
C. Lazzaro,
50
P. Leaci,
90
,
32
S. Leavey,
43
C. H. Lee,
86
H. K. Lee,
127
H. M. Lee,
121
H. W. Lee,
122
K. Lee,
43
J. Lehmann,
9
A. Lenon,
37
,
38
M. Leonardi,
102
,
89
N. Leroy,
26
N. Letendre,
7
Y. Levin,
126
T. G. F. Li,
87
A. Libson,
14
T. B. Littenberg,
128
J. Liu,
60
R. K. L. Lo,
87
N. A. Lockerbie,
117
L. T. London,
95
J. E. Lord,
41
M. Lorenzini,
16
,
17
V. Loriette,
129
M. Lormand,
6
G. Losurdo,
23
J. D. Lough,
9
,
21
C. O. Lousto,
115
G. Lovelace,
27
H. L ̈uck,
21
,
9
D. Lumaca,
30
,
17
A. P. Lundgren,
9
R. Lynch,
14
Y. Ma,
59
S. Macfoy,
58
B. Machenschalk,
9
M. MacInnis,
14
D. M. Macleod,
2
I. Maga ̃na Hernandez,
87
F. Maga ̃na-Sandoval,
41
L. Maga ̃na Zertuche,
41
R. M. Magee,
82
E. Majorana,
32
I. Maksimovic,
129
N. Man,
62
V. Mandic,
42
V. Mangano,
43
G. L. Mansell,
24
M. Manske,
20
M. Mantovani,
28
F. Marchesoni,
48
,
40
F. Marion,
7
S. M ́arka,
46
Z. M ́arka,
46
C. Markakis,
11
A. S. Markosyan,
47
E. Maros,
1
F. Martelli,
65
,
66
L. Martellini,
62
I. W. Martin,
43
D. V. Martynov,
14
K. Mason,
14
A. Masserot,
7
T. J. Massinger,
1
M. Masso-Reid,
43
S. Mastrogiovanni,
90
,
32
A. Matas,
42
F. Matichard,
14
L. Matone,
46
N. Mavalvala,
14
N. Mazumder,
64
R. McCarthy,
44
D. E. McClelland,
24
S. McCormick,
6
L. McCuller,
14
S. C. McGuire,
130
G. McIntyre,
1
J. McIver,
1
D. J. McManus,
24
T. McRae,
24
S. T. McWilliams,
37
,
38
D. Meacher,
82
G. D. Meadors,
34
,
9
J. Meidam,
13
E. Mejuto-Villa,
8
A. Melatos,
131
G. Mendell,
44
R. A. Mercer,
20
E. L. Merilh,
44
M. Merzougui,
62
S. Meshkov,
1
C. Messenger,
43
C. Messick,
82
R. Metzdorff,
68
P. M. Meyers,
42
F. Mezzani,
32
,
90
H. Miao,
53
C. Michel,
25
H. Middleton,
53
E. E. Mikhailov,
132
L. Milano,
75
,
4
A. L. Miller,
5
A. Miller,
90
,
32
B. B. Miller,
94
J. Miller,
14
M. Millhouse,
93
O. Minazzoli,
62
Y. Minenkov,
17
J. Ming,
34
C. Mishra,
133
S. Mitra,
18
V. P. Mitrofanov,
57
G. Mitselmakher,
5
R. Mittleman,
14
A. Moggi,
23
M. Mohan,
28
S. R. P. Mohapatra,
14
M. Montani,
65
,
66
B. C. Moore,
103
C. J. Moore,
12
D. Moraru,
44
G. Moreno,
44
S. R. Morriss,
97
B. Mours,
7
C. M. Mow-Lowry,
53
G. Mueller,
5
A. W. Muir,
95
Arunava Mukherjee,
9
D. Mukherjee,
20
S. Mukherjee,
97
N. Mukund,
18
A. Mullavey,
6
J. Munch,
78
E. A. M. Muniz,
41
P. G. Murray,
43
K. Napier,
73
I. Nardecchia,
30
,
17
L. Naticchioni,
90
,
32
R. K. Nayak,
134
G. Nelemans,
61
,
13
T. J. N. Nelson,
6
M. Neri,
54
,
55
M. Nery,
9
A. Neunzert,
113
J. M. Newport,
114
G. Newton
‡
,
43
K. K. Y. Ng,
87
T. T. Nguyen,
24
D. Nichols,
61
A. B. Nielsen,
9
S. Nissanke,
61
,
13
A. Nitz,
9
A. Noack,
9
F. Nocera,
28
D. Nolting,
6
M. E. N. Normandin,
97
L. K. Nuttall,
41
J. Oberling,
44
E. Ochsner,
20
E. Oelker,
14
G. H. Ogin,
106
J. J. Oh,
123
S. H. Oh,
123
F. Ohme,
9
M. Oliver,
96
P. Oppermann,
9
Richard J. Oram,
6
B. O’Reilly,
6
R. Ormiston,
42
L. F. Ortega,
5
R. O’Shaughnessy,
115
D. J. Ottaway,
78
H. Overmier,
6
B. J. Owen,
80
A. E. Pace,
82
J. Page,
128
M. A. Page,
60
A. Pai,
109
S. A. Pai,
56
J. R. Palamos,
67
O. Palashov,
120
C. Palomba,
32
A. Pal-Singh,
31
H. Pan,
83
B. Pang,
59
P. T. H. Pang,
87
C. Pankow,
94
F. Pannarale,
95
B. C. Pant,
56
F. Paoletti,
23
A. Paoli,
28
M. A. Papa,
34
,
20
,
9
H. R. Paris,
47
W. Parker,
6
D. Pascucci,
43
A. Pasqualetti,
28
R. Passaquieti,
22
,
23
D. Passuello,
23
B. Patricelli,
135
,
23
B. L. Pearlstone,
43
M. Pedraza,
1
R. Pedurand,
25
,
136
L. Pekowsky,
41
A. Pele,
6
S. Penn,
137
C. J. Perez,
44
A. Perreca,
1
,
102
,
89
L. M. Perri,
94
H. P. Pfeiffer,
105
M. Phelps,
43
O. J. Piccinni,
90
,
32
M. Pichot,
62
F. Piergiovanni,
65
,
66
V. Pierro,
8
G. Pillant,
28
L. Pinard,
25
I. M. Pinto,
8
M. Pitkin,
43
R. Poggiani,
22
,
23
P. Popolizio,
28
E. K. Porter,
35
A. Post,
9
J. Powell,
43
J. Prasad,
18
J. W. W. Pratt,
33
V. Predoi,
95
3
T. Prestegard,
20
M. Prijatelj,
9
M. Principe,
8
S. Privitera,
34
R. Prix,
9
G. A. Prodi,
102
,
89
L. G. Prokhorov,
57
O. Puncken,
9
M. Punturo,
40
P. Puppo,
32
M. P ̈urrer,
34
H. Qi,
20
J. Qin,
60
S. Qiu,
126
V. Quetschke,
97
E. A. Quintero,
1
R. Quitzow-James,
67
F. J. Raab,
44
D. S. Rabeling,
24
H. Radkins,
44
P. Raffai,
51
S. Raja,
56
C. Rajan,
56
M. Rakhmanov,
97
K. E. Ramirez,
97
P. Rapagnani,
90
,
32
V. Raymond,
34
M. Razzano,
22
,
23
J. Read,
27
T. Regimbau,
62
L. Rei,
55
S. Reid,
58
D. H. Reitze,
1
,
5
H. Rew,
132
S. D. Reyes,
41
F. Ricci,
90
,
32
P. M. Ricker,
11
S. Rieger,
9
K. Riles,
113
M. Rizzo,
115
N. A. Robertson,
1
,
43
R. Robie,
43
F. Robinet,
26
A. Rocchi,
17
L. Rolland,
7
J. G. Rollins,
1
V. J. Roma,
67
J. D. Romano,
97
R. Romano,
3
,
4
C. L. Romel,
44
J. H. Romie,
6
D. Rosi ́nska,
138
,
52
M. P. Ross,
139
S. Rowan,
43
A. R ̈udiger,
9
P. Ruggi,
28
K. Ryan,
44
S. Sachdev,
1
T. Sadecki,
44
L. Sadeghian,
20
M. Sakellariadou,
140
L. Salconi,
28
M. Saleem,
109
F. Salemi,
9
A. Samajdar,
134
L. Sammut,
126
L. M. Sampson,
94
E. J. Sanchez,
1
V. Sandberg,
44
B. Sandeen,
94
J. R. Sanders,
41
B. Sassolas,
25
P. R. Saulson,
41
O. Sauter,
113
R. L. Savage,
44
A. Sawadsky,
21
P. Schale,
67
J. Scheuer,
94
E. Schmidt,
33
J. Schmidt,
9
P. Schmidt,
1
,
61
R. Schnabel,
31
R. M. S. Schofield,
67
A. Sch ̈onbeck,
31
E. Schreiber,
9
D. Schuette,
9
,
21
B. W. Schulte,
9
B. F. Schutz,
95
,
9
S. G. Schwalbe,
33
J. Scott,
43
S. M. Scott,
24
E. Seidel,
11
D. Sellers,
6
A. S. Sengupta,
141
D. Sentenac,
28
V. Sequino,
30
,
17
A. Sergeev,
120
D. A. Shaddock,
24
T. J. Shaffer,
44
A. A. Shah,
128
M. S. Shahriar,
94
L. Shao,
34
B. Shapiro,
47
P. Shawhan,
72
A. Sheperd,
20
D. H. Shoemaker,
14
D. M. Shoemaker,
73
K. Siellez,
73
X. Siemens,
20
M. Sieniawska,
52
D. Sigg,
44
A. D. Silva,
15
A. Singer,
1
L. P. Singer,
76
A. Singh,
34
,
9
,
21
R. Singh,
2
A. Singhal,
16
,
32
A. M. Sintes,
96
B. J. J. Slagmolen,
24
B. Smith,
6
J. R. Smith,
27
R. J. E. Smith,
1
E. J. Son,
123
J. A. Sonnenberg,
20
B. Sorazu,
43
F. Sorrentino,
55
T. Souradeep,
18
A. P. Spencer,
43
A. K. Srivastava,
99
A. Staley,
46
D.A. Steer,
35
M. Steinke,
9
J. Steinlechner,
43
,
31
S. Steinlechner,
31
D. Steinmeyer,
9
,
21
B. C. Stephens,
20
R. Stone,
97
K. A. Strain,
43
G. Stratta,
65
,
66
S. E. Strigin,
57
R. Sturani,
142
A. L. Stuver,
6
T. Z. Summerscales,
143
L. Sun,
131
S. Sunil,
99
P. J. Sutton,
95
B. L. Swinkels,
28
M. J. Szczepa ́nczyk,
33
M. Tacca,
35
D. Talukder,
67
D. B. Tanner,
5
M. T ́apai,
110
A. Taracchini,
34
J. A. Taylor,
128
R. Taylor,
1
T. Theeg,
9
E. G. Thomas,
53
M. Thomas,
6
P. Thomas,
44
K. A. Thorne,
6
K. S. Thorne,
59
E. Thrane,
126
S. Tiwari,
16
,
89
V. Tiwari,
95
K. V. Tokmakov,
117
K. Toland,
43
M. Tonelli,
22
,
23
Z. Tornasi,
43
C. I. Torrie,
1
D. T ̈oyr ̈a,
53
F. Travasso,
28
,
40
G. Traylor,
6
D. Trifir`o,
10
J. Trinastic,
5
M. C. Tringali,
102
,
89
L. Trozzo,
144
,
23
K. W. Tsang,
13
M. Tse,
14
R. Tso,
1
D. Tuyenbayev,
97
K. Ueno,
20
D. Ugolini,
145
C. S. Unnikrishnan,
111
A. L. Urban,
1
S. A. Usman,
95
H. Vahlbruch,
21
G. Vajente,
1
G. Valdes,
97
M. Vallisneri,
59
N. van Bakel,
13
M. van Beuzekom,
13
J. F. J. van den Brand,
71
,
13
C. Van Den Broeck,
13
D. C. Vander-Hyde,
41
L. van der Schaaf,
13
J. V. van Heijningen,
13
A. A. van Veggel,
43
M. Vardaro,
49
,
50
V. Varma,
59
S. Vass,
1
M. Vas ́uth,
45
A. Vecchio,
53
G. Vedovato,
50
J. Veitch,
53
P. J. Veitch,
78
K. Venkateswara,
139
G. Venugopalan,
1
D. Verkindt,
7
F. Vetrano,
65
,
66
A. Vicer ́e,
65
,
66
A. D. Viets,
20
S. Vinciguerra,
53
D. J. Vine,
58
J.-Y. Vinet,
62
S. Vitale,
14
T. Vo,
41
H. Vocca,
39
,
40
C. Vorvick,
44
D. V. Voss,
5
W. D. Vousden,
53
S. P. Vyatchanin,
57
A. R. Wade,
1
L. E. Wade,
81
M. Wade,
81
R. Walet,
13
M. Walker,
2
L. Wallace,
1
S. Walsh,
20
G. Wang,
16
,
66
H. Wang,
53
J. Z. Wang,
82
M. Wang,
53
Y.-F. Wang,
87
Y. Wang,
60
R. L. Ward,
24
J. Warner,
44
M. Was,
7
J. Watchi,
91
B. Weaver,
44
L.-W. Wei,
9
,
21
M. Weinert,
9
A. J. Weinstein,
1
R. Weiss,
14
L. Wen,
60
E. K. Wessel,
11
P. Weßels,
9
T. Westphal,
9
K. Wette,
9
J. T. Whelan,
115
B. F. Whiting,
5
C. Whittle,
126
D. Williams,
43
R. D. Williams,
1
A. R. Williamson,
115
J. L. Willis,
146
B. Willke,
21
,
9
M. H. Wimmer,
9
,
21
W. Winkler,
9
C. C. Wipf,
1
H. Wittel,
9
,
21
G. Woan,
43
J. Woehler,
9
J. Wofford,
115
K. W. K. Wong,
87
J. Worden,
44
J. L. Wright,
43
D. S. Wu,
9
G. Wu,
6
W. Yam,
14
H. Yamamoto,
1
C. C. Yancey,
72
M. J. Yap,
24
Hang Yu,
14
Haocun Yu,
14
M. Yvert,
7
A. Zadro ̇zny,
124
M. Zanolin,
33
T. Zelenova,
28
J.-P. Zendri,
50
M. Zevin,
94
L. Zhang,
1
M. Zhang,
132
T. Zhang,
43
Y.-H. Zhang,
115
C. Zhao,
60
M. Zhou,
94
Z. Zhou,
94
S. J. Zhu,
34
,
9
X. J. Zhu,
60
M. E. Zucker,
1
,
14
and J. Zweizig
1
(LIGO Scientific Collaboration and Virgo Collaboration)
∗
Deceased, March 2016.
‡
Deceased, December 2016.
†
Deceased,
February 2017.
♯
Deceased, March 2017.
§
Deceased, November 2017.
1
LIGO, California Institute of Technology, Pasadena, CA 911
25, USA
2
Louisiana State University, Baton Rouge, LA 70803, USA
3
Universit`a di Salerno, Fisciano, I-84084 Salerno, Italy
4
INFN, Sezione di Napoli, Complesso Universitario di Monte S
.Angelo, I-80126 Napoli, Italy
5
University of Florida, Gainesville, FL 32611, USA
6
LIGO Livingston Observatory, Livingston, LA 70754, USA
7
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy
, France
8
University of Sannio at Benevento, I-82100 Benevento,
Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
9
Albert-Einstein-Institut, Max-Planck-Institut f ̈ur Gra
vitationsphysik, D-30167 Hannover, Germany
4
10
The University of Mississippi, University, MS 38677, USA
11
NCSA, University of Illinois at Urbana-Champaign, Urbana,
IL 61801, USA
12
University of Cambridge, Cambridge CB2 1TN, United Kingdom
13
Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands
14
LIGO, Massachusetts Institute of Technology, Cambridge, M
A 02139, USA
15
Instituto Nacional de Pesquisas Espaciais, 12227-010 S ̃ao
Jos ́e dos Campos, S ̃ao Paulo, Brazil
16
Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Ita
ly
17
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
18
Inter-University Centre for Astronomy and Astrophysics, P
une 411007, India
19
International Centre for Theoretical Sciences, Tata Insti
tute of Fundamental Research, Bengaluru 560089, India
20
University of Wisconsin-Milwaukee, Milwaukee, WI 53201, U
SA
21
Leibniz Universit ̈at Hannover, D-30167 Hannover, Germany
22
Universit`a di Pisa, I-56127 Pisa, Italy
23
INFN, Sezione di Pisa, I-56127 Pisa, Italy
24
OzGrav, Australian National University, Canberra, Austra
lian Capital Territory 0200, Australia
25
Laboratoire des Mat ́eriaux Avanc ́es (LMA), CNRS/IN2P3, F-
69622 Villeurbanne, France
26
LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit ́e Paris-Sacl
ay, F-91898 Orsay, France
27
California State University Fullerton, Fullerton, CA 9283
1, USA
28
European Gravitational Observatory (EGO), I-56021 Cascin
a, Pisa, Italy
29
Chennai Mathematical Institute, Chennai 603103, India
30
Universit`a di Roma Tor Vergata, I-00133 Roma, Italy
31
Universit ̈at Hamburg, D-22761 Hamburg, Germany
32
INFN, Sezione di Roma, I-00185 Roma, Italy
33
Embry-Riddle Aeronautical University, Prescott, AZ 86301
, USA
34
Albert-Einstein-Institut, Max-Planck-Institut f ̈ur Gra
vitationsphysik, D-14476 Potsdam-Golm, Germany
35
APC, AstroParticule et Cosmologie, Universit ́e Paris Dide
rot,
CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,
Sorbonne Paris Cit ́e, F-75205 Paris Cedex 13, France
36
Korea Institute of Science and Technology Information, Dae
jeon 34141, Korea
37
West Virginia University, Morgantown, WV 26506, USA
38
Center for Gravitational Waves and Cosmology,
West Virginia University, Morgantown, WV 26505, USA
39
Universit`a di Perugia, I-06123 Perugia, Italy
40
INFN, Sezione di Perugia, I-06123 Perugia, Italy
41
Syracuse University, Syracuse, NY 13244, USA
42
University of Minnesota, Minneapolis, MN 55455, USA
43
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdo
m
44
LIGO Hanford Observatory, Richland, WA 99352, USA
45
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl ́os ́u
t 29-33, Hungary
46
Columbia University, New York, NY 10027, USA
47
Stanford University, Stanford, CA 94305, USA
48
Universit`a di Camerino, Dipartimento di Fisica, I-62032 C
amerino, Italy
49
Universit`a di Padova, Dipartimento di Fisica e Astronomia
, I-35131 Padova, Italy
50
INFN, Sezione di Padova, I-35131 Padova, Italy
51
MTA E ̈otv ̈os University, “Lendulet” Astrophysics Researc
h Group, Budapest 1117, Hungary
52
Nicolaus Copernicus Astronomical Center, Polish Academy o
f Sciences, 00-716, Warsaw, Poland
53
University of Birmingham, Birmingham B15 2TT, United Kingd
om
54
Universit`a degli Studi di Genova, I-16146 Genova, Italy
55
INFN, Sezione di Genova, I-16146 Genova, Italy
56
RRCAT, Indore MP 452013, India
57
Faculty of Physics, Lomonosov Moscow State University, Mos
cow 119991, Russia
58
SUPA, University of the West of Scotland, Paisley PA1 2BE, Un
ited Kingdom
59
Caltech CaRT, Pasadena, CA 91125, USA
60
OzGrav, University of Western Australia, Crawley, Western
Australia 6009, Australia
61
Department of Astrophysics/IMAPP, Radboud University Nij
megen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
62
Artemis, Universit ́e Cˆote d’Azur, Observatoire Cˆote d’A
zur,
CNRS, CS 34229, F-06304 Nice Cedex 4, France
63
Institut de Physique de Rennes, CNRS, Universit ́e de Rennes
1, F-35042 Rennes, France
64
Washington State University, Pullman, WA 99164, USA
65
Universit`a degli Studi di Urbino ’Carlo Bo’, I-61029 Urbin
o, Italy
66
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenz
e, Italy
67
University of Oregon, Eugene, OR 97403, USA
5
68
Laboratoire Kastler Brossel, UPMC-Sorbonne Universit ́es
, CNRS,
ENS-PSL Research University, Coll`ege de France, F-75005 P
aris, France
69
Carleton College, Northfield, MN 55057, USA
70
Astronomical Observatory Warsaw University, 00-478 Warsa
w, Poland
71
VU University Amsterdam, 1081 HV Amsterdam, The Netherland
s
72
University of Maryland, College Park, MD 20742, USA
73
Center for Relativistic Astrophysics and School of Physics
,
Georgia Institute of Technology, Atlanta, GA 30332, USA
74
Universit ́e Claude Bernard Lyon 1, F-69622 Villeurbanne, F
rance
75
Universit`a di Napoli ’Federico II’, Complesso Universita
rio di Monte S.Angelo, I-80126 Napoli, Italy
76
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
77
RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.
78
OzGrav, University of Adelaide, Adelaide, South Australia
5005, Australia
79
Tsinghua University, Beijing 100084, China
80
Texas Tech University, Lubbock, TX 79409, USA
81
Kenyon College, Gambier, OH 43022, USA
82
The Pennsylvania State University, University Park, PA 168
02, USA
83
National Tsing Hua University, Hsinchu City, 30013 Taiwan,
Republic of China
84
Charles Sturt University, Wagga Wagga, New South Wales 2678
, Australia
85
University of Chicago, Chicago, IL 60637, USA
86
Pusan National University, Busan 46241, Korea
87
The Chinese University of Hong Kong, Shatin, NT, Hong Kong
88
INAF, Osservatorio Astronomico di Padova, Vicolo dell’Oss
ervatorio 5, I-35122 Padova, Italy
89
INFN, Trento Institute for Fundamental Physics and Applica
tions, I-38123 Povo, Trento, Italy
90
Universit`a di Roma ’La Sapienza’, I-00185 Roma, Italy
91
Universit ́e Libre de Bruxelles, Brussels 1050, Belgium
92
Sonoma State University, Rohnert Park, CA 94928, USA
93
Montana State University, Bozeman, MT 59717, USA
94
Center for Interdisciplinary Exploration & Research in Ast
rophysics (CIERA),
Northwestern University, Evanston, IL 60208, USA
95
Cardiff University, Cardiff CF24 3AA, United Kingdom
96
Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma
de Mallorca, Spain
97
The University of Texas Rio Grande Valley, Brownsville, TX 7
8520, USA
98
Bellevue College, Bellevue, WA 98007, USA
99
Institute for Plasma Research, Bhat, Gandhinagar 382428, I
ndia
100
The University of Sheffield, Sheffield S10 2TN, United Kingdom
101
California State University, Los Angeles, 5151 State Unive
rsity Dr, Los Angeles, CA 90032, USA
102
Universit`a di Trento, Dipartimento di Fisica, I-38123 Pov
o, Trento, Italy
103
Montclair State University, Montclair, NJ 07043, USA
104
National Astronomical Observatory of Japan, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan
105
Canadian Institute for Theoretical Astrophysics,
University of Toronto, Toronto, Ontario M5S 3H8, Canada
106
Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
107
School of Mathematics, University of Edinburgh, Edinburgh
EH9 3FD, United Kingdom
108
University and Institute of Advanced Research, Gandhinaga
r Gujarat 382007, India
109
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
110
University of Szeged, D ́om t ́er 9, Szeged 6720, Hungary
111
Tata Institute of Fundamental Research, Mumbai 400005, Ind
ia
112
INAF, Osservatorio Astronomico di Capodimonte, I-80131, N
apoli, Italy
113
University of Michigan, Ann Arbor, MI 48109, USA
114
American University, Washington, D.C. 20016, USA
115
Rochester Institute of Technology, Rochester, NY 14623, US
A
116
University of Bia lystok, 15-424 Bia lystok, Poland
117
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kin
gdom
118
University of Southampton, Southampton SO17 1BJ, United Ki
ngdom
119
University of Washington Bothell, 18115 Campus Way NE, Both
ell, WA 98011, USA
120
Institute of Applied Physics, Nizhny Novgorod, 603950, Rus
sia
121
Seoul National University, Seoul 08826, Korea
122
Inje University Gimhae, South Gyeongsang 50834, Korea
123
National Institute for Mathematical Sciences, Daejeon 340
47, Korea
124
NCBJ, 05-400
́
Swierk-Otwock, Poland
125
Institute of Mathematics, Polish Academy of Sciences, 0065
6 Warsaw, Poland
126
OzGrav, School of Physics & Astronomy, Monash University, C
layton 3800, Victoria, Australia
127
Hanyang University, Seoul 04763, Korea
6
128
NASA Marshall Space Flight Center, Huntsville, AL 35811, US
A
129
ESPCI, CNRS, F-75005 Paris, France
130
Southern University and A&M College, Baton Rouge, LA 70813,
USA
131
OzGrav, University of Melbourne, Parkville, Victoria 3010
, Australia
132
College of William and Mary, Williamsburg, VA 23187, USA
133
Indian Institute of Technology Madras, Chennai 600036, Ind
ia
134
IISER-Kolkata, Mohanpur, West Bengal 741252, India
135
Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 P
isa, Italy
136
Universit ́e de Lyon, F-69361 Lyon, France
137
Hobart and William Smith Colleges, Geneva, NY 14456, USA
138
Janusz Gil Institute of Astronomy, University of Zielona G ́o
ra, 65-265 Zielona G ́ora, Poland
139
University of Washington, Seattle, WA 98195, USA
140
King’s College London, University of London, London WC2R 2L
S, United Kingdom
141
Indian Institute of Technology, Gandhinagar Ahmedabad Guj
arat 382424, India
142
International Institute of Physics, Universidade Federal
do Rio Grande do Norte, Natal RN 59078-970, Brazil
143
Andrews University, Berrien Springs, MI 49104, USA
144
Universit`a di Siena, I-53100 Siena, Italy
145
Trinity University, San Antonio, TX 78212, USA
146
Abilene Christian University, Abilene, TX 79699, USA
Cosmic strings are topological defects which can be formed i
n GUT-scale phase transitions in
the early universe. They are also predicted to form in the con
text of string theory. The main
mechanism for a network of Nambu-Goto cosmic strings to lose
energy is through the production of
loops and the subsequent emission of gravitational waves, t
hus offering an experimental signature
for the existence of cosmic strings. Here we report on the ana
lysis conducted to specifically search
for gravitational-wave bursts from cosmic string loops in t
he data of Advanced LIGO 2015-2016
observing run (O1). No evidence of such signals was found in t
he data, and as a result we set upper
limits on the cosmic string parameters for three recent loop
distribution models. In this paper, we
initially derive constraints on the string tension
Gμ
and the intercommutation probability, using not
only the burst analysis performed on the O1 data set, but also
results from the previously published
LIGO stochastic O1 analysis, pulsar timing arrays, cosmic m
icrowave background and Big-Bang
nucleosynthesis experiments. We show that these data sets a
re complementary in that they probe
gravitational waves produced by cosmic string loops during
very different epochs. Finally, we show
that the data sets exclude large parts of the parameter space
of the three loop distribution models
we consider.
PACS numbers: 11.27.+d, 98.80.Cq, 11.25.-w
I. INTRODUCTION
The recent observation of gravitational waves [1]
(GWs) has started a new era in astronomy [2, 3]. In the
coming years Advanced LIGO [4] and Advanced Virgo [5]
will be targeting a wide variety of GW sources [6]. Some
of these potential sources could yield new physics and
information about the universe at its earliest moments.
This would be the case for the observation of GWs from
cosmic strings, which are one-dimensional topological de-
fects, formed after a spontaneous symmetry phase tran-
sition characterized by a vacuum manifold with non-
contractible loops. Cosmic strings were first introduced
by Kibble [7], (for a review see for instance [8–10]). They
can be generically produced in the context of Grand Uni-
fied Theories [11]. Linear-type topological defects of dif-
ferent forms should leave a variety of observational signa-
tures, opening up a fascinating window to fundamental
physics at very high energy scales. In particular, they
should lens distant galaxies [12–14], produce high energy
cosmic rays [15], lead to anisotropies in the cosmic mi-
crowave background [16, 17], and produce GWs [18, 19].
A network of cosmic strings is primarily characterized
by the string tension
Gμ
(
c
= 1), where
G
is Newton’s
constant and
μ
the mass per unit length. The existence of
cosmic strings can be tested using the cosmic microwave
background (CMB) measurements. Confronting experi-
mental CMB data with numerical simulations of cosmic
string networks [20–23], the string tension is constrained
to be smaller than a few 10
−
7
.
Cosmic superstrings are coherent macroscopic states of
fundamental superstrings (F-strings) and also D-branes
extended in one macroscopic direction (D-strings). They
are predicted in superstring inspired inflationary models
with spacetime-wrapping D-branes [24, 25]. For cosmic
superstrings, one must introduce another parameter to
account for the fact that they interact probabilistically.
In [26], it is suggested that this intercommutation proba-
bility
p
must take values between 10
−
1
and 1 for D-strings
and between 10
−
3
and 1 for F-strings. In this paper, we
will refer to both topological strings and superstrings as
“strings”, and parameterize them by
p
and
Gμ
.
Cosmic string parameters can also be accessed through
GWs. Indeed, the dynamics of the network is driven
by the formation of loops and the emission of GWs. In
particular, cusps and kinks propagating on string loops
7
are expected to produce powerful bursts of GWs. The
superposition of these bursts gives rise to a stochastic
background which can be probed over a large range of
frequencies by different observations. Historically, the
Big-Bang nucleosynthesis (BBN) data provided the first
constraints on cosmic strings [27]. It was then surpassed
by CMB bounds [28] to then be surpassed more recently
by pulsar timing bounds [29]. In this paper, we report
on the search for GW burst signals produced by cos-
mic string cusps and kinks using Advanced LIGO data
collected between September 12, 2015 06:00 UTC and
January 19, 2016 17:00 UTC [30], offering a total of
T
obs
= 4 163 421 s (
∼
48
.
2 days) of coincident data be-
tween the two LIGO detectors. Moreover, combining
the result from the stochastic GW background search
previously published in [31], we test and constrain cos-
mic string models. While the LIGO O1 burst limit re-
mains weak, the stochastic bound now surpasses the BBN
bound for the first time and is competitive with the CMB
bound across much of the parameter space.
We will place constraints on the most up-to-date string
loop distributions. In particular, we select three analytic
cosmic string models (
M
=
{
1
,
2
,
3
}
) [8, 32–35] for the
number density of string loops, developed in part from
numerical simulations of Nambu-Goto string networks
(zero thickness strings with intercommutation probabil-
ity equal to unity), in a Friedman-Lemaˆıtre-Robertson-
Walker geometry. These models are more fully described
in Sec. II where their fundamental differences are also dis-
cussed. Sec. III presents an overview of the experimental
data sets which are used to constrain the cosmic string
parameters. Finally, the resulting limits are discussed in
Sec. IV.
II. COSMIC STRING MODELS
We constrain three different models of cosmic strings
indexed by
M
. Common to all these models is the as-
sumption that the width of the strings is negligible com-
pared to the size of the horizon, so that the string dy-
namics is given by the Nambu-Goto action. A further
input is the strings intercommutation probability
p
. For
field theory strings, and in particular
U
(1) Abelian-Higgs
strings in the Bogomol’nyi–Prasad–Sommerfield limit [8],
intercommutation occurs with effectively unit probability
[36, 37],
p
= 1. That is, when two super-horizon (infi-
nite) strings intersect, they always swap partners; and
if a string intersects itself, it therefore chops off a (sub-
horizon) loop. The latter can also result from string-
string intersections at two points, leading to the forma-
tion of two new infinite strings and a loop.
Cosmic string loops oscillate periodically in time, emit-
ting GWs
1
. A loop of invariant length
ℓ
, has pe-
1
Super-horizon cosmic strings also emit GWs, due to their sma
ll-
scale structure [19, 38, 39].
riod
T
=
ℓ/
2 and corresponding fundamental frequency
ω
= 4
π/ℓ
. As a result it radiates GWs with frequen-
cies which are multiples of
ω
, and decays in a lifetime
τ
=
ℓ/γ
d
where [18, 40, 41]
γ
d
≡
Γ
Gμ
with Γ
≃
50
.
(1)
If a loop contains kinks [41–43] (discontinuities on the
tangent vector of a string) and cusps (points where the
string instantaneously reaches the speed of light), these
source bursts of beamed GWs [44–46]. The incoherent
superposition of these bursts give rise to a stationary
and nearly Gaussian stochastic GW background. Occa-
sionally, sharp and high-amplitude bursts of GWs stand
above this stochastic GW background.
The three models considered here differ in the loop dis-
tribution
n
(
ℓ, t
)
dℓ
, namely the number density of cosmic
string loops of invariant length between
ℓ
and
ℓ
+
dℓ
at
cosmic time
t
. To determine the consequences of these
differences on their GW signal, we work in units of cosmic
time
t
and introduce the dimensionless variables
γ
≡
ℓ/t
and
F
(
γ, t
)
≡
n
(
ℓ, t
)
×
t
4
.
(2)
We will often refer to
γ
as the relative size of loops and
F
as simply the loop distribution. All GWs observed to-
day are formed when the string network is in its
scaling
regime
, namely a self-similar, attractor solution in which
all the typical length scales in the problem are propor-
tional to cosmic time
2
.
The models considered here were developed (in part)
using numerical simulations of Nambu-Goto strings, for
which
p
= 1. As mentioned above, cosmic superstrings
intercommute with probability
p <
1. The effect of a
reduced intercommutation probability on the loop distri-
bution has been studied in [47]. Following this reference
we take
F
p<
1
=
F
/p
3
, leading to an increased density
of strings [48] and to an enhancement of various obser-
vational signatures.
A. Model
M
= 1
: original large loop distribution
The first model we consider is the oldest, developed in
[8, 32]. It assumes that, in the scaling regime, all loops
chopped off the infinite string network are formed with
the
same
relative size, which we denote by
α
. At time
t
, the distribution of loops of length
ℓ
to
ℓ
+
dℓ
contains
loops chopped off the infinite string network at earlier
times, and diluted by the expansion of the universe and
2
Scaling breaks down for a short time in the transition betwee
n
the radiation and matter eras, and similarly in the transiti
on to
dark energy domination.
3
In [47] the exponent of the power law behavior was found to be
slightly different, namely 0.6. Since our goal here is to high
light
the effect of
p <
1, we used a simple dependence of 1
/p
as many
others in the litterature have done.